Description
Compare displacement calculated before and after subtracting a common supplied origin.
A vector is an ordered set of components in a chosen basis. Its norm measures magnitude, while dot products, projections, and coordinate transformations describe different relationships. Component order, angle units, normalization, and numerical tolerances determine the meaning of a computed result.
Compare displacement calculated before and after subtracting a common supplied origin.
When to use this tool
Use Vector Origin Change Direction Invariance when you need the particular coordinate operation, derivative, residual, or domain check under a known basis convention.
How to use the tool and how it works
- Enter start, end, origin. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read direction, shiftedDirection. Use the output convention below.
Require aligned start, end, and origin arrays. Return direction=end-start and shiftedDirection=(end-origin)-(start-origin) componentwise.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| start | Start | Required. Array of Finite number.; maximum items 256. |
| end | End | Required. Array of Finite number.; maximum items 256. |
| origin | Origin | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| direction | Direction | Required. Array of Finite number.; maximum items 256. |
| shiftedDirection | Shifted Direction | Required. Array of Finite number.; maximum items 256. |
{
"input": {
"start": [
1,
2
],
"end": [
4,
6
],
"origin": [
10,
20
]
},
"output": {
"direction": [
3,
4
],
"shiftedDirection": [
3,
4
]
}
}Limitations and assumptions
- The expressions are algebraically equal but may differ through floating-point cancellation, especially for large origins. The tool reports both without asserting exact equality or estimating a numerical error bound.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Choose a complete vector or matrix operation when a single component or residual is insufficient. For sensitive near-zero or near-singular cases, inspect numerical conditioning and use an appropriate precision and tolerance.
References
Similar or alternative tools
- Vector Affine Origin Shift Budget
Passive coordinate change to a new origin displaced by a supplied vector.
- Vector: Vector Affine Point Direction Tag
Encode a 2D/3D affine point or free direction into homogeneous coordinates with explicit final weight one or zero; no projective division.